Due to the nature of the data that is accumulated in social networking services, there are a great variety of data-driven uses. However, private information occasionally gets published within sanitized datasets offered to third parties. In this paper we consider a strong class of deanonymization attacks that can re-identify these datasets using structural information crawled from other networks. We provide the model level analysis of a technique called identity separation that could be used for hiding information even from these attacks. We show that in case of noncollaborating users ca. 50% of them need to adopt the technique in order to tackle re-identification over the network. We additionally highlight several settings of the technique that allows preserving privacy on the personal level. In the second part of our experiments we evaluate a measure of anonymity, and show that if users with low anonymity values apply identity separation, the minimum adoption rate for repelling the attack drops down to 3 - 15 %. Additionally, we show that it is necessary for top degree nodes to participate.